PRP Records

Probable Primes Top 10000

(202622 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
9751(102^25087-1)/10150388Richard Fischer08/2017
975235^32629-783450382Enzo Doria03/2013
97546^64744+16350381Lelio R Paula06/2012
9753116447#+17465950381Nicolas PALAU09/2016
97552^167353+12950379Lelio R Paula05/2009
975620^38722-113350379Enzo Doria03/2013
97573^105567-1650369Lelio R Paula07/2012
97582^167321-11284950369Enzo Doria06/2014
9759(28*10^50362-43)/350363Robert Price04/2016
976011421^12410-12410^1142150357Norbert Schneider08/2013
97612^167278-206350356Yves Minet03/2013
9762181^22300+22300^18150347Serge Batalov05/2014
97639932^12595-12595^993250343Norbert Schneider12/2016
97648993^12732-12732^899350342Norbert Schneider02/2017
97653*5^72018-450339Lelio R Paula09/2014
97662^167207-11268750335Enzo Doria06/2014
97676^64674-3750327Lelio R Paula06/2012
97682^167177+7480150326Enzo Doria04/2016
976913739^4600+4600^1373950323Hans Havermann10/2015
977011508^12391+12391^1150850320Norbert Schneider06/2014
97712^167132-216350312Yves Minet08/2013
97727^59527-6250307Lelio R Paula06/2012
9774(310027^9161+1)/31002850302Faysal YAtim04/2008
9773(12301^12301+74)/3^2/5^3/11/17/115150302Makoto Morimoto07/2016
97752^167083-11251950297Enzo Doria06/2014
9776272^20659-20659^27250296Norbert Schneider09/2015
977725337!!-1650290Robert Price06/2015
97789722^12611-12611^972250290Norbert Schneider12/2016
9779(15*2^167013+1)/64950275Lelio R Paula07/2012
978019^39315-1250275Lelio R Paula01/2013
97815^71925-3650274Lelio R Paula06/2012
97822^167002+279913950273Enzo Doria04/2016
978310957^12444-12444^1095750270Norbert Schneider07/2013
97848*10^50253-9950254Robert Price02/2017
97865^71894-5450252Lelio R Paula06/2012
9785(127^23887+1)/12850252Richard Fischer04/2017
978718^40028-550247Lelio R Paula01/2013
9788(3*2^166904+1)/127950241Lelio R Paula07/2012
978924^36397+2350236Norbert Schneider12/2013
97907984*29^34345+2150230Curtis Bright05/2015
97913^105248-1352850217Enzo Doria02/2013
97926^64532-6550216Lelio R Paula06/2012
97935^71834-2061650210Enzo Doria03/2013
9794(31*2^166778-1)/365150204Lelio R Paula01/2014
97952^166752-11239750198Enzo Doria06/2014
9796(12277^12277+1746)/17/37/15150197Makoto Morimoto07/2016
979711^48199-93050195Enzo Doria11/2012
97983*10^50194-750195Erik Branger11/2013
97999992^12549+12549^999250192Norbert Schneider10/2015
98002^166708+15750185Lelio R Paula01/2011
9801(1338272^8192+1)/6553750184Syoichiro Yamada06/2008
98027*2^166685+350179Lelio R Paula02/2014
98037*2^166671-950174Lelio R Paula02/2014
98049*2^166670+750174Lelio R Paula02/2014
98052^166670-11254150173Enzo Doria06/2014
98066149^13242-13242^614950172Norbert Schneider01/2018
98072^166657+46550169Lelio R Paula11/2011
980817^40768-2050163Lelio R Paula01/2013
98092^166596-7879550151Lelio R Paula07/2011
9810135^23541+13450151Norbert Schneider04/2015
981124^36335-67350150Enzo Doria03/2013
9812(12269^12269+291)/2^8/5/7/19/41/109/1042634950150Makoto Morimoto07/2016
9813(52*10^50149+119)/950150Robert Price10/2017
9814(28*10^50147-97)/350148Robert Price07/2016
9815263^20718-20718^26350137Norbert Schneider09/2015
9816t(167020)50133Robert Price01/2015
9817(12263^12263+1442)/127/547950133Makoto Morimoto07/2016
98182868*(2340*(29023#-29527)*(2340*(29023#-29527)+3)+1)*(2868*(2340*(29023#-29527)*(2340*(29023#-29527)50129Pierre CAMI06/2008
981912^46445-1950123Lelio R Paula12/2012
98202^166501-1459350122Enzo Doria04/2013
9821(31*2^166509-1)/368407750120Lelio R Paula01/2014
98222^166483-16950117Lelio R Paula01/2011
9823(188^22037+1)/18950114Eric Chen09/2017
98249^52515+2*6^52515-4^5251550113Mike Oakes04/2010
9825(23*2^166487-1)/3377049950112Lelio R Paula01/2014
98262*5^71689-950109Lelio R Paula09/2014
982713495^5154+5154^1349550096Hans Havermann04/2016
98296^64369-11950089Lelio R Paula06/2012
98289224^12633-12633^922450089Norbert Schneider12/2016
98302^166370-11254150083Enzo Doria06/2014
9831(12253^12253+1454)/3^3/251/947/29242750081Makoto Morimoto07/2016
98322^166339-11232150074Enzo Doria06/2014
98335^71637-2250073Lelio R Paula06/2012
9834Phi(50131,10)/89010999409/9123691040118653/18020045580157867/3062191531806380194750068Maksym Voznyy01/2013
9835(4*10^50060+137)/350061Robert Price07/2017
98365^71618-1382650059Enzo Doria02/2013
983715^42563-250058Lelio R Paula11/2012
98381943^15222+15222^194350058Serge Batalov05/2014
9839183^22125-250057Lelio R Paula10/2017
984011641^12310+12310^1164150053Norbert Schneider04/2014
984113537!-2^13537+150052Joe McLean06/2006
98422^166227-16446750040Gary Barnes08/2009
984312241^12241+475650039Makoto Morimoto07/2016
9844(106*10^50035-1)/350037Serge Batalov12/2014
984511^48044-81050033Enzo Doria11/2012
984615^42539+8850030Lelio R Paula11/2012
9847524^18397-523^1839750028Jean-Louis Charton10/2009
98482^166159-1449750019Enzo Doria04/2013
98492^166155+8785550018Lelio R Paula01/2009
98502^166138-1165550013Lelio R Paula07/2011
9851(L(239313)-1)/5-2^955150013Jorge Menendez06/2017
98526487^13118-13118^648750007Norbert Schneider10/2017
9853(16*10^50005+41)/350006Robert Price10/2017
98582^166104-11262550003Enzo Doria06/2014
9854(L(239265)-1)/5-2^90650003Jorge Menendez03/2017
9855(L(239265)-1)/5-2^315250003Jorge Menendez04/2017
9856(L(239265)-1)/5-2^2015550003Jorge Menendez04/2017
9857(L(239265)-1)/5-2^7891250003Jorge Menendez04/2017
98592^166100+19901550002Lelio R Paula05/2008
986510^50000+6585950001Milton L. Brown02/2006
9860(598*10^49999-31)/950001Robert Price02/2017
986110^50000+581092721613350001Jorge Menendez09/2017
986210^50000+581092760537750001Jorge Menendez09/2017
986310^50000+581092765837950001Jorge Menendez09/2017
986410^50000+581092767222350001Jorge Menendez09/2017
986610^49999+9170150000Patrick De Geest03/2005
988610^50000-19430350000Patrick De Geest02/2009
9867(2^74207281/10^948782)%10^5000050000Michael Vang04/2016
9868(2^57885161/10^11608093)%10^5000050000Michael Vang05/2016
9869(2^43112609/10^788658)%10^5000050000Michael Vang05/2016
9870(2^42643801/10^3670320)%10^5000050000Michael Vang05/2016
9871(2^37156667/10^412682)%10^5000050000Michael Vang05/2016
9872(2^32582657/10^7836670)%10^5000050000Michael Vang05/2016
9873(2^24036583/10^3069021)%10^5000050000Michael Vang05/2016
9874(2^25964951/10^5214128)%10^5000050000Michael Vang05/2016
9875(2^13466917/10^157937)%10^5000050000Michael Vang05/2016
9876(2^20996011/10^6193479)%10^5000050000Michael Vang05/2016
9877(2^6972593/10^381525)%10^5000050000Michael Vang05/2016
9878(2^30402457/10^1629036)%10^5000050000Michael Vang05/2016
9879(2^3021377/10^702316)%10^5000050000Michael Vang05/2016
9880(2^1398269/10^37827)%10^5000050000Michael Vang05/2016
9881(2^2976221/10^767789)%10^5000050000Michael Vang05/2016
9882(2^859433/10^42285)%10^5000050000Michael Vang06/2016
9883(2^1257787/10^119173)%10^5000050000Michael Vang06/2016
9884(2^756839/10^136257)%10^5000050000Michael Vang06/2016
98852*10^49999+36350000Makoto Morimoto09/2016
988710^49999-414949999Patrick De Geest02/2009
988810484^12433-12433^1048449988Norbert Schneider07/2013
98892^166052+14549987Lelio R Paula01/2011
9890(10^50001+10936)/(2^3*19*241*5872003*15974507)49983Makoto Morimoto09/2016
98911111*2^166022-55549981Henri Lifchitz02/2005
989211^47993+3049980Lelio R Paula10/2012
98932^166000-7879549971Lelio R Paula07/2011
989413517!-13517#+14997003/2005
98962^165995-11322749970Enzo Doria07/2014
9895(12227^12227+1092)/5/11/17/37^249970Makoto Morimoto07/2016
989717^40609+1449968Lelio R Paula11/2012
9898(1257656^8192+1)/6553749963Syoichiro Yamada06/2008
9899(3^104735-8)/149319993149963Lelio R Paula03/2012
99002^165969-11271149962Enzo Doria06/2014
99012^165910-760549944Lelio R Paula04/2009
990236313!3-5904949942Robert Price12/2015
99032^165884-4549937Lelio R Paula08/2010
9904(1246892^8192+1)/6553749933Syoichiro Yamada06/2008
99053^104654+10449933Lelio R Paula07/2012
99067452^12895-12895^745249933Norbert Schneider05/2017
99079035^12622+12622^903549932Norbert Schneider01/2016
9908(22699*2^165838+1)/328749924Lelio R Paula05/2014
99096^64149-8549918Lelio R Paula06/2012
9910(7*10^49913+71)/349914Robert Price03/2016
99112^165799-11481749911Enzo Doria05/2015
99122^165789+3549908Lelio R Paula08/2010
99132^165783-12149906Lelio R Paula01/2011
99142^165760-11264949899Enzo Doria06/2014
9915(11*2^165758+1)/13549898Lelio R Paula01/2012
99162^165747+6349895Lelio R Paula04/2009
9917(7*10^49893-13)/349894Robert Price06/2016
9918298^20163-20163^29849888Norbert Schneider08/2015
9919(49885^49885)/(10^184474)49885James G. Merickel08/2015
992017^40540+3649883Lelio R Paula11/2012
9921(12211^12211+4312)/13/17/31/1297/1483/1627/9923/3643349882Makoto Morimoto07/2016
99222^165676-11294949874Enzo Doria06/2014
9923(12203^12203+992)/1149867Makoto Morimoto07/2016
99247784^12811-12811^778449851Norbert Schneider03/2017
99252^165581-74549845Yves Minet01/2012
99262^165576+7482149844Enzo Doria04/2016
992713318^5527+5527^1331849843Hans Havermann04/2016
99292^165561-215549839Yves Minet08/2013
9928(12197^12197+1755)/2^449839Makoto Morimoto07/2016
99307406^12879+12879^740649837Norbert Schneider03/2016
99318530^12677+12677^853049833Norbert Schneider01/2016
9932(3^52222-69)^2-7149833Jorge Menendez02/2017
993312^46175+2949832Lelio R Paula10/2012
99342^165488-1296949817Enzo Doria10/2012
99352^165473+5890549813Lelio R Paula04/2009
993620^38284+4949809Lelio R Paula11/2012
99383^104388-2049806Lelio R Paula07/2012
9937(10^49806+119)/349806Serge Batalov12/2014
9939(1202206^8192+1)/6553749803Syoichiro Yamada06/2008
9940(4*10^49801+11)/349802Erik Branger05/2013
99415^71240-1547649795Enzo Doria02/2013
99427*3^104334-449781Lelio R Paula03/2014
9943(136*10^49774-1)/949776Serge Batalov12/2014
99443^104297+868049763Lelio R Paula07/2012
9945(F(10)^28579-F(9)^28579)/F(8)49737Wayne Halsdorf03/2010
9946(3^104243+1)/449736Kamil Duszenko05/2004
9947(10223*2^165183+1)/5549728Lelio R Paula05/2014
99486^63895+10149720Lelio R Paula06/2012
99493^104194+10049714Lelio R Paula07/2012
995010^49711+10359349712Patrick De Geest07/2017
995110^49711-70149711Robert Price06/2017
9952U(356793)49710Serge Batalov03/2015
995313321^5388+5388^1332149707Hans Havermann04/2016
995412166^12166+56549700Henri Lifchitz11/2004
9955(89*10^49689-53)/949690Erik Branger05/2013
9956(1163126^8192+1)/6553749685Syoichiro Yamada06/2008
995711^47709+4249684Lelio R Paula10/2012
9958(35*10^49682+1)/949683Serge Batalov05/2010
9959(12163^12163+1194)/37/19349683Makoto Morimoto07/2016
99603^104124+9249680Lelio R Paula07/2012
99612^165025+16502949678Henri Lifchitz04/2005
996214063^3408+3408^1406349678Hans Havermann04/2016
9963(2^165031+3)/4843949675Lelio R Paula01/2012
9964(7*2^165020-1)/26149675Lelio R Paula01/2014
9965(155^22679+1)/15649673Eric Chen12/2017
99672^165000+522749670Lelio R Paula05/2011
9966(12161^12161+765)/2/13/29/277/31149670Makoto Morimoto07/2016
9968(110051^9851+1)/11005249660Faysal YAtim09/2007
99692^164962-63979149659Paul Bourdelais11/2012
997010^49657+3149658Robert Price01/2011
997110^49657-1289949657Patrick De Geest01/2012
99722^164937-19349651Lelio R Paula01/2011
997321^37549-20^3754949649Jean-Louis Charton02/2012
99741417^15754+15754^141749647Serge Batalov05/2014
9975(12157^12157+2611)/2^5/11/13/1019/48197/31440749643Makoto Morimoto07/2016
997612^45999+2549642Lelio R Paula10/2012
9977(3^104040+7)/849639Lelio R Paula03/2012
99782^164882-101749635Lelio R Paula06/2008
9979(3^104053-8)/38183002074345549632Lelio R Paula03/2012
998011^47658-18049631Enzo Doria07/2012
99812^164859-123749628Yves Minet08/2012
998217^40331+9849626Lelio R Paula11/2012
99831638^15437+15437^163849620Serge Batalov05/2014
9984113^24160+11249603Norbert Schneider09/2013
998513^44527+1649601Lelio R Paula11/2012
998683^25844+8249597Norbert Schneider01/2013
9987(12143^12143+1306)/3/7/5949593Makoto Morimoto07/2016
9988114667#-p(114667)49591Henri Lifchitz03/2007
99892^164731-183384749589Enzo Doria05/2015
9990(625^17737+1)/62649588Richard Fischer06/2013
99922^164714+2983549584Lelio R Paula11/2011
9991(38*10^49583+187)/949584Robert Price11/2017
99937*10^49580-6949581Robert Price01/2017
99947*5^70922+449574Lelio R Paula09/2014
9995(229*10^49571-1)/349573Robert Price12/2016
9996277^20295-29049571Enzo Doria06/2012
99972^164662-11288349569Enzo Doria06/2014
9998(1125424^8192+1)/6553749568Syoichiro Yamada06/2008
99996^63698-3549567Lelio R Paula06/2012
10000(2^164652-3)*6-749566Gilbert Mozzo04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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